Problem: Solve for $x$ and $y$ using elimination. ${3x+y = 32}$ ${5x-y = 40}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. $8x = 72$ $\dfrac{8x}{{8}} = \dfrac{72}{{8}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {3x+y = 32}\thinspace$ to find $y$ ${3}{(9)}{ + y = 32}$ $27+y = 32$ $27{-27} + y = 32{-27}$ ${y = 5}$ You can also plug ${x = 9}$ into $\thinspace {5x-y = 40}\thinspace$ and get the same answer for $y$ : ${5}{(9)}{ - y = 40}$ ${y = 5}$